The baby, who will not be an HRH, will be born 15th in line to the throne, with their great-uncle, the Duke of Edinburgh, moving down to 16th place.
He or she will also be the 15th great-grandchild of the late Queen Elizabeth II, and the third to be born since her death in 2022.
The announcement from Buckingham Palace, which posted the news on its social media channel at 10am, will be seen as a show of support for Eugenie despite the troubles surrounding her shamed father.
Andrew — the King’s brother — was arrested on suspicion of misconduct in public office in February amid the scandal surrounding his friendship with the vile pedo Jeffrey Epstein.
Eugenie and her sister Beatrice, who has two children Sienna, four, and Athena, one, stayed away from the traditional royal gathering on Easter Sunday, with the agreement of Charles, amid the furore over their father.